Math Problem Statement
If KL = 8x, LM = 14x - 6, and KM = 16, what is KL?
Solution
We are given that:
Since lie on a straight line, the sum of and must equal :
Substitute the given expressions for , , and :
Simplify the left-hand side:
Now, solve for :
Now that we have , we can find :
Thus, .
Would you like further details on this solution?
Here are some related questions for you to explore:
- What is the value of when ?
- What is the total length of ?
- How would the result change if instead of 16?
- Can you represent this problem geometrically on a number line?
- What would happen if instead?
Tip: When dealing with line segments, always remember that the sum of smaller segments must equal the total length of the larger segment.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Geometry (Line Segments)
Formulas
KL + LM = KM
Solving for x in linear equations
Theorems
Segment Addition Postulate (the sum of smaller segments equals the total segment)
Suitable Grade Level
Grades 6-8